According to quantum theory, a measurement may have multiple possible outcomes. Single-world interpretations assert that, nevertheless, only one of them "really" occurs. Here we propose a gedankenexperiment where quantum theory is applied to model an experimenter who herself uses quantum theory. We find that, in such a scenario, no single-world interpretation can be logically consistent. This conclusion extends to deterministic hidden-variable theories, such as Bohmian mechanics, for they impose a single-world interpretation.
Hat tip: https://boffosocko.com/2019/01/01/frauchiger-renner-paradox-clarifies-where-our-views-of-reality-go-wrong-quanta-magazine/
Michael Atiyah, a famed UK mathematician, claims that he has a "simple proof" of the Riemann hypothesis, a key unsolved question about the nature of prime numbers
Logical probability theory was developed as a quantitative measure based on Boole's logic of subsets. But information theory was developed into a mature theory by Claude Shannon with no such connection to logic. But a recent development in logic changes this situation. In category theory, the notion of a subset is dual to the notion of a quotient set or partition, and recently the logic of partitions has been developed in a parallel relationship to the Boolean logic of subsets (subset logic is usually mis-specified as the special case of propositional logic). What then is the quantitative measure based on partition logic in the same sense that logical probability theory is based on subset logic? It is a measure of information that is named "logical entropy" in view of that logical basis. This paper develops the notion of logical entropy and the basic notions of the resulting logical information theory. Then an extensive comparison is made with the corresponding notions based on Shannon entropy.
Ellerman is visiting at UC Riverside at the moment. Given the information theory and category theory overlap, I'm curious if he's working with John Carlos Baez, or what Baez is aware of this. Based on a cursory look of his website(s), I'm going to have to start following more of this work.
For the rapidly decreasing amount of space I've got for storing and actively using the handful of machines I've got in my burgeoning typewriter collection, I've begun to become a bit more discerning of new acquisitions. I had yet to add a Royal the fleet, and I've had my eye on a handful, but the…
I purchased this SCM typewriter through an online auction on 2024-03-02 and received it this morning on 2024-03-07 at 10:00 AM. The seller stated this was a 1969, but the Typewriter Database doesn't seem to have serial number dating for this range of typewriters which were manufactured between 1966 and 1972. I doubt the seller…
Someone was having a sale, so I might have just spent $18.65 for a massive haul of 4,500 4 x 6" index cards. 🗃️ Happy New Year indeed!🥂🎆🥳
Robert Hutchins, former dean of Yale Law School (1927–1929), president (1929–1945) and chancellor (1945–1951) of the University of Chicago, closes his preface to his grand project with Mortimer J. Adler by giving pride of place to Adler's Syntopicon. It touches on the unreasonable value of building and maintaining a zettelkasten: But I would do less…
Over the weekend I had the good fortune to hear about a little stationery shop 10 minutes from my house. Baum-kuchen is a spectacular little space hiding over on Lincoln in Altadena with a warm, wabi-sabi (わびさび) charm. The business began in 2010, but opened up their physical location in 2019. Obviously not the most…
Childhood Typewriters I've had a hollow space in my chest where a typewriter wanted to be. I'd had a few inexpensive plastic ones in my childhood before having a really spectacular Smith-Corona, but I thought that through many moves it had been long lost. Until, that is, I visited my parents on spring break this…
I've been watching the secondary market for used card indexes for a while and finally caved and purchased a vintage wooden desk top Shaw-Walker 11 inch card index for 3 x 5" index cards. It was dusty and dirty and in reasonably good shape, but with some cleaning and some wood polish, it's in much…
The Steelcase Vintage Quidditch Chair
It was overdue for re-upholstery, so I picked up some material yesterday and recovered my 1950's Steelcase chair. The finish on this one is in okay shape, but I really want to refinish both it and its twin which I spent a bit of time cleaning up yesterday. It's now been redubbed the Quidditch chair…
I thought it might be useful to have a relatively complete list of cross linked topical headings in my digital notebook (currently Obsidian) which is a mélange of wiki, zettelkasten, journal, project management tool, notebook, and productivity tool. First, let's be honest that mélange is too poetic based on what I see of how others…
For those who don't want to create a Zotero account for the tools for thought group, here's the list as of 2022-05-07. It doesn't include the tags, folder structure, or related Zotero meta data, but it will give an idea of some of the current contents. We're happy to provide credentials to the group for…
Starting an experiment of the month, and succumbing to my curiosity around Python.
I love how the tired old link log idea has been re-framed here as a learning log. I might have to borrow the idea for my digital commonplace book. I'm also glad to have stumbled across this so serendipitously for its mention of WaniKani for learning 日本語 (Japanese) kanji. I'm not quite sure what to…
David Ellerman
Melanie Richards